Experimental Mathematics

Yet More Projective Curves over \field{2}

Chris Lomont

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Abstract

All plane curves of degree less than 7 with coefficients in $\field{2}$ are examined for curves with a large number of $\field{q}$ rational points on their smooth model, for $q=2^m, m = 3,4,...,11$. Known lower bounds are improved, and new curves are found meeting or close to Serre's, Lauter's, and Ihara's upper bounds for the maximal number of $\field{q}$ rational points on a curve of genus g.

Article information

Source
Experiment. Math., Volume 11, Issue 4 (2002), 547-554.

Dates
First available in Project Euclid: 10 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1057864663

Mathematical Reviews number (MathSciNet)
MR1969645

Zentralblatt MATH identifier
1101.14305

Subjects
Primary: 14H45: Special curves and curves of low genus
Secondary: 11T71: Algebraic coding theory; cryptography 94B

Keywords
Error correcting codes low genus curves curves over finite fields

Citation

Lomont, Chris. Yet More Projective Curves over \field{2}. Experiment. Math. 11 (2002), no. 4, 547--554. https://projecteuclid.org/euclid.em/1057864663


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